Spatially Selective Active Noise Control for Open-fitting Hearables with Acausal Optimization

TL;DR

This work addresses the challenge of preserving desired speech while suppressing undesired noise for open-fitting hearables operating in spatially complex environments. It introduces acausal relative impulse responses into the spatially selective active noise control (SSANC) optimization, deriving a closed-form solution for the anti-noise filter and showing that $L_a>0$ systematically outperforms the causal case ($L_a=0$). Across two anechoic-scenario simulations, the acausal approach achieves markedly lower speech distortion and higher noise reduction and SNR improvements, with an effective acausal window around $L_a\approx12$. The results demonstrate that acausal ReIRs provide a more accurate representation of the desired source, enabling robust noise control and improved intelligibility in wearable audio devices.

Abstract

Recent advances in active noise control have enabled the development of hearables with spatial selectivity, which actively suppress undesired noise while preserving desired sound from specific directions. In this work, we propose an improved approach to spatially selective active noise control that incorporates acausal relative impulse responses into the optimization process, resulting in significantly improved performance over the causal design. We evaluate the system through simulations using a pair of open-fitting hearables with spatially localized speech and noise sources in an anechoic environment. Performance is evaluated in terms of speech distortion, noise reduction, and signal-to-noise ratio improvement across different delays and degrees of acausality. Results show that the proposed acausal optimization consistently outperforms the causal approach across all metrics and scenarios, as acausal filters more effectively characterize the response of the desired source.

Figures (6)

• Figure 1: Block diagram of an ANC system with $K$ outer microphones, one inner error microphone and one loudspeaker (i.e., secondary source). The control filter is denoted by $\mathbf{w}$, the secondary path is denoted by $\mathbf{g}$, and its estimate by $\widehat{\mathbf{g}}$.
• Figure 2: (a) Illustration of the open-fitting hearable. (b) First acoustic scenario. A desired speech source is at $0^\circ$, and one undesired speech source is at $45^\circ$. (c) Second acoustic scenario. The desired speech source is at $0^\circ$, and five babble noise sources are at $45^\circ$, $90^\circ$, $135^\circ$, $255^\circ$ and $330^\circ$.
• Figure 3: Speech distortion, noise reduction, and SNR improvement for the first simulation scenario for different delay $\Delta$ when (a) $L_a = 0$ and $L_a=22$, with $\beta = \lambda_\mathrm{max} (\mathbf{G}^\mathcal{T} \bm{\Phi}_{{\mathbf{x}} {\mathbf{x}}} \mathbf{G} ) / (5.0e3) = \lambda_1 / (5.0e3)$, (b) $L_a = 0$ and $L_a=22$, with $\beta = \lambda_1 / (2.0e6)$. In all cases, $\rho = \lambda_\mathrm{max} (\mathbf{H} \mathbf{G} \bm{\Phi}_{\mathbf{rr}}^{-1} \mathbf{G}^\mathcal{T} \mathbf{H}^\mathcal{T}) / (1.0e5)$.
• Figure 4: Speech distortion, noise reduction, and SNR improvement for the second simulation scenario for different delay $\Delta$ when $L_a = 0$, $\beta = \lambda_1 / (4.0e3)$, and when $L_a=22$, $\beta = \lambda_1 / (4.0e7)$. In both cases, $\rho = \lambda_\mathrm{max} (\mathbf{H} \mathbf{G} \bm{\Phi}_{\mathbf{rr}}^{-1} \mathbf{G}^\mathcal{T} \mathbf{H}^\mathcal{T}) / (2.0e5)$.
• Figure 5: Speech distortion, noise reduction, and SNR improvement for the first simulation scenario for different $L_a$ values when $\Delta = 32$, $\beta = \lambda_1 / (2.0e6)$ and $\rho = \lambda_\mathrm{max} (\mathbf{H} \mathbf{G} \bm{\Phi}_{\mathbf{rr}}^{-1} \mathbf{G}^\mathcal{T} \mathbf{H}^\mathcal{T}) / (1.0e5)$.